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If F(x+y) = F(x) * F(y) Given : F(3) = 729

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If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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New post 05 Apr 2018, 08:42
5
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

38% (02:59) correct 62% (02:22) wrong based on 34 sessions

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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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New post 05 Apr 2018, 08:58
2
1
IMO C.

Nice tricky Q.
F(3/2) = F(1 + 1/2) = F(1)*F(1/2) .. similarly F(1) = F(1/2)*F(1/2)

So question can be restated as ... What is F(1/2) + F(1/2)^2 + F(1/2)^3

Now we need to simplify the given info.
F(3)
= F(1+2) = F(2)*F(1) = F(1)*F(1)*F(1) ...F(2) = F(1+1) = F(1)*F(1)
=729

F(1)^3 = 9^3 (...729)
F(1) = 9
F(1) = F(1/2 +1/2) = F(1/2)^2 =9
F(1/2) = 3. I am discarding the negative roots based on the answer choices... As all are positive !

So..
Question is :
3 + 3^2 + 3^3 = 3 + 9 + 27 = 39.

Hence Option (c) is our answer.

Best,
Gladi

Kudos for this answer please..!! :-D



gmatbusters wrote:
If F(x+y) = F(x) * F(y)
Given :
F(3) = 729

Find
F(1/2) +F(1) +F(3/2) = ?

A. 13
B. 27
C. 39
D. 52
E. 81

_________________
Regards,
Gladi



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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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New post 05 Apr 2018, 10:06
gmatbusters wrote:
If F(x+y) = F(x) * F(y)
Given :
F(3) = 729

Find
F(1/2) +F(1) +F(3/2) = ?

A. 13
B. 27
C. 39
D. 52
E. 81



from this equation we can tell that
\(F(x) = (F(1)) ^n\)
F(3)=F(1)^3
F(1)=9
\(F(1/2)=F(1)^1/2\)=3
\(F(3/2)=F(1)^3/2\)=27

39
option C
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Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729  [#permalink]

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New post 05 Apr 2018, 17:19
4
F(3) = F(3/2 + 3/2) = F(3/2) * F(3/2) = [F(3/2)]^2 = 729 --> F(3/2) = 27

F(3) = F(1 + 1 + 1) = F(1) * F(1) * F(1) = [F(1)]^3 = 729 --> F(1) = 9

F(1) = F(1/2 + 1/2) = F(1/2) * F(1/2) = [F(1/2)]^2 = 9 --> F(1/2) = 3

F(1/2) +F(1) +F(3/2) = 3 + 9 + 27 = 39

Answer: C
GMAT Club Bot
Re: If F(x+y) = F(x) * F(y) Given : F(3) = 729   [#permalink] 05 Apr 2018, 17:19
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